Quick summary:
- Technically you need a valid US passport to enter the US
- As a US citizen, you can't be denied entry, which is in direct conflict with rule #1 above. In practice, most likely you will get in, however the CBP (Customs and Border Protection) can make the process miserable for you.
- No airline will let you board a flight to the US with an expired US passport and they have every right to deny you boarding if you don't have proper paperwork.